Under Administer > Customize Data and Screens > Date Preferences, CiviCRM offers a number of date classes for which an administrator can specify date formats. activityDate is described as "Date for activities including contributions: receive, receipt, cancel. membership: join, start, renew. case: start, end." activityDateTime is described as "Date and time for activity: scheduled. participant: registered."
Where are these settings actually used? I changed the date format for both of these, cleared CiviCRM's caches, and headed over to the contact summary, expecting to see the new date formats on the Activities and Contributions tabs. Instead, I found no change at all.